Finite Group Databasebeta

← C3×#30431 #10649038

Subgroups — C3×#30431 #10649038

Order 768.

912 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3061C211yesmaximal, characteristic, complemented
2C3×#3060C211yesmaximal, characteristic, complemented
3C3×#3012C211yesmaximal, characteristic, complemented
4C3×#3012C211yesmaximal, characteristic, complemented
5C3×#2092C211yesmaximal, characteristic, complemented
6C3×#2079C211yesmaximal, characteristic, complemented
7C3×#2078C211yesmaximal, characteristic, complemented
8C3×#2040C211yesmaximal, characteristic, complemented
9C3×#2040C211yesmaximal, characteristic, complemented
10C3×#2006C211yesmaximal, characteristic, complemented
11C3×#1907C211yesmaximal, characteristic, complemented
12C3×#1907C211yesmaximal, characteristic, complemented
13C3×#1876C211yesmaximal, characteristic, complemented
14C3×#1876C211yesmaximal, characteristic, complemented
15C3×#1792C211yesmaximal, characteristic, complemented
16#30431C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C3×#135C2211yescharacteristic
21C2×C3×#135C2211yescharacteristic
22C2×C3×#131C2211yescharacteristic, complemented
23C2×C3×#131C2211yescharacteristic, complemented
24C3×#537C2211yescharacteristic
25C3×#537C2211yescharacteristic
26C3×#537C2211yescharacteristic, complemented
27C3×#470—21no—
28C3×#469—21no—
29C3×#468—21no—
30C3×#468—21no—
31C3×#467—21no—
32C3×#466—21no—
33C3×#465—21no—
34C3×#465—21no—
35C3×#452—21no—
36C3×#452—21no—
37C3×#450—21no—
38C3×#450—21no—
39C3×#449—21no—
40C3×#449—21no—
41C3×#447—21no—
42C3×#447—21no—
43C2×C3×#107C2211yescharacteristic, complemented
44C2×C3×#106C2211yescharacteristic, complemented
45C2×C3×#104C2211yescharacteristic
46C2×C3×#104C2211yescharacteristic
47C2×C3×#104C2211yescharacteristic, complemented
48C2×C3×#104C2211yescharacteristic, complemented
49C3×#417C2211yescharacteristic
50C3×#417C2211yescharacteristic
51C3×#417C2211yescharacteristic
52C3×#417C2211yescharacteristic
53C3×#417C2211yescharacteristic, complemented
54C3×#417C2211yescharacteristic, complemented
55C2×C3×#102C2211yescharacteristic
56C2×C3×#102C2211yescharacteristic
57C2×C3×#100C2211yescharacteristic
58C3×#408C2211yescharacteristic
59C3×#408C2211yescharacteristic
60C3×#390C2211yescharacteristic
61C3×#382C2211yescharacteristic, complemented
62C3×#343C2211yescharacteristic, complemented
63C3×#343C2211yescharacteristic, complemented
64C3×#343C2211yescharacteristic, complemented
65C3×#341C2211yescharacteristic, complemented
66C3×#341C2211yescharacteristic, complemented
67C3×#336C2211yescharacteristic, complemented
68#3061C2×C311yescharacteristic, complemented
69#3060C2×C311yescharacteristic, complemented
70#3012C2×C311yescharacteristic, complemented
71#3012C2×C311yescharacteristic, complemented
72#2092C2×C311yescharacteristic, complemented
73#2079C2×C311yescharacteristic, complemented
74#2078C2×C311yescharacteristic, complemented
75#2040C2×C311yescharacteristic, complemented
76#2040C2×C311yescharacteristic, complemented
77#2006C2×C311yescharacteristic, complemented
78#1907C2×C311yescharacteristic, complemented
79#1907C2×C311yescharacteristic, complemented
80#1876C2×C311yescharacteristic, complemented
81#1876C2×C311yescharacteristic, complemented
82#1792C2×C311yescharacteristic, complemented
83C3×H(5,𝔽2)—22no—
84C3×H(5,𝔽2)—41no—
85C3×H(5,𝔽2)—41no—
86C3×H(5,𝔽2)—41no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41C2311yescharacteristic
90C2×C3×#41C2311yescharacteristic
91C2×C3×#41C2311yescharacteristic
92C2×C3×#41C2311yescharacteristic
93C22×C3×D4—21no—
94C22×C3×D4—21no—
95C22×C3×D4—41no—
96C22×C3×D4C2311yescharacteristic
97C3×AGL(1,ℤ/8)—22no—
98C3×AGL(1,ℤ/8)—22no—
99C3×AGL(1,ℤ/8)—41no—
100C3×AGL(1,ℤ/8)—41no—
101C3×#135—41no—
102C3×#135—41no—
103C3×#135—41no—
104C3×#135—41no—
105C2×C3×Q16D411yescharacteristic
106C2×C3×Q16D411yescharacteristic
107C2×C3×SD16—21no—
108C2×C3×SD16—21no—
109C2×C3×SD16D411yescharacteristic
110C2×C3×SD16D411yescharacteristic
111C2×C3×SD16D411yescharacteristic
112C2×C3×SD16D411yescharacteristic
113C2×C3×D8—21no—
114C2×C3×D8—21no—
115C2×C3×D8D411yescharacteristic
116C2×C3×D8D411yescharacteristic
117C3×#131—41no—
118C3×#131—41no—
119C3×#131—41no—
120C3×#131—41no—
121C2×C3×M16—21no—
122C2×C3×M16—21no—
123C2×C3×M16C2311yescharacteristic
124C2×C3×M16C2311yescharacteristic
125C2×C3×M16C2311yescharacteristic
126C2×C3×M16C2311yescharacteristic
127C22×C3×C8—21no—
128C22×C3×C8—21no—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—21no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—21no—
142C3×#121—21no—
143C3×#121—41no—
144C3×#121—41no—
145C3×#121—41no—
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4—41no—
150C2×C3×C42C2311yescharacteristic
151C3×#107—21no—
152C3×#107—21no—
153C3×#106—21no—
154C3×#106—21no—
155C3×#104—41no—
156C3×#104—41no—
157C3×#104—41no—
158C3×#104—41no—
159C3×#103—21no—
160C3×#103—21no—
161C3×#103—21no—
162C3×#103—21no—
163C3×#103—21no—
164C3×#103—21no—
165C3×#102—21no—
166C3×#102—21no—
167C3×#102—21no—
168C3×#102—21no—
169C3×#102—21no—
170C3×#102—21no—
171C3×#102—21no—
172C3×#102—21no—
173C3×#102—21no—
174C3×#102—21no—
175C3×#100—41no—
176C3×C22⋊C8—21no—
177C3×C22⋊C8—21no—
178C3×C22⋊C8—21no—
179C3×C22⋊C8—21no—
180C3×#95—41no—
181C2×H(5,𝔽2)C22×C311yescharacteristic
182C2×AGL(1,ℤ/8)C22×C311yescharacteristic
183C2×AGL(1,ℤ/8)C22×C311yescharacteristic
184C2×#135C22×C311yescharacteristic
185C2×#135C22×C311yescharacteristic
186C2×#131C22×C311yescharacteristic, complemented
187C2×#131C22×C311yescharacteristic, complemented
188#537C22×C311yescharacteristic
189#537C22×C311yescharacteristic
190#537C22×C311yescharacteristic, complemented
191#470—21no—
192#469—21no—
193#468—21no—
194#468—21no—
195#467—21no—
196#466—21no—
197#465—21no—
198#465—21no—
199#452—21no—
200#452—21no—
201#450—21no—
202#450—21no—
203#449—21no—
204#449—21no—
205#447—21no—
206#447—21no—
207C2×#107C22×C311yescharacteristic, complemented
208C2×#106C22×C311yescharacteristic, complemented
209C2×#104C22×C311yescharacteristic
210C2×#104C22×C311yescharacteristic
211C2×#104C22×C311yescharacteristic, complemented
212C2×#104C22×C311yescharacteristic, complemented
213#417C22×C311yescharacteristic
214#417C22×C311yescharacteristic
215#417C22×C311yescharacteristic
216#417C22×C311yescharacteristic
217#417C22×C311yescharacteristic, complemented
218#417C22×C311yescharacteristic, complemented
219C2×#102C22×C311yescharacteristic
220C2×#102C22×C311yescharacteristic
221C2×#100C22×C311yescharacteristic
222#408C22×C311yescharacteristic
223#408C22×C311yescharacteristic
224#390C22×C311yescharacteristic
225#382C22×C311yescharacteristic, complemented
226#343C22×C311yescharacteristic, complemented
227#343C22×C311yescharacteristic, complemented
228#343C22×C311yescharacteristic, complemented
229#341C22×C311yescharacteristic, complemented
230#341C22×C311yescharacteristic, complemented
231#336C22×C311yescharacteristic, complemented
232C24×C3—21no—
233C24×C3—41no—
234C3×#41—21no—
235C3×#41—21no—
236C3×#41—21no—
237C3×#41—21no—
238C3×#41—21no—
239C3×#41—21no—
240C3×#41—21no—
241C3×#41—21no—
242C3×#41—21no—
243C3×#41—21no—
244C3×#41—21no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41—21no—
250C3×#41—42no—
251C3×#41—42no—
252C3×#41—42no—
253C3×#41—42no—
254C2×C3×Q8C2×D411yescharacteristic
255C2×C3×Q8C2×D411yescharacteristic
256C2×C3×Q8C2×D411yescharacteristic
257C2×C3×Q8C2×D411yescharacteristic
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—41no—
268C2×C3×D4—41no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—41no—
276C2×C3×D4—41no—
277C2×C3×D4—41no—
278C2×C3×D4C2×D411yescharacteristic
279C2×C3×D4C2×D411yescharacteristic
280C2×C3×D4C2×D411yescharacteristic
281C2×C3×D4C2×D411yescharacteristic
282C2×C3×D4#4112yes—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—41no—
292C22×C3×C4C2411yescharacteristic
293C3×Q16—41no—
294C3×Q16—41no—
295C3×SD16—41no—
296C3×SD16—41no—
297C3×SD16—41no—
298C3×SD16—41no—
299C3×SD16—42no—
300C3×SD16—42no—
301C3×D8—41no—
302C3×D8—41no—
303C3×D8—42no—
304C3×D8—42no—
305C3×M16—21no—
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—42no—
314C3×M16—42no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—42no—
324C2×C3×C8—42no—
325C2×C3×C8C2×D411yescharacteristic
326C2×C3×C8C2×D411yescharacteristic
327C2×C3×C8C2×D411yescharacteristic
328C2×C3×C8C2×D411yescharacteristic
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—41no—
338C3×C22⋊C4—41no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—41no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—41no—
343C3×C22⋊C4—41no—
344C3×C22⋊C4—82no—
345C3×C42—21no—
346C3×C42—21no—
347H(5,𝔽2)—22no—
348H(5,𝔽2)—41no—
349H(5,𝔽2)—41no—
350H(5,𝔽2)—41no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41C23×C311yescharacteristic
354C2×#41C23×C311yescharacteristic
355C2×#41C23×C311yescharacteristic
356C2×#41C23×C311yescharacteristic
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—41no—
360C22×D4C23×C311yescharacteristic
361AGL(1,ℤ/8)—22no—
362AGL(1,ℤ/8)—22no—
363AGL(1,ℤ/8)—41no—
364AGL(1,ℤ/8)—41no—
365#135—41no—
366#135—41no—
367#135—41no—
368#135—41no—
369C2×Q16C3×D411yescharacteristic
370C2×Q16C3×D411yescharacteristic
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16C3×D411yescharacteristic
374C2×SD16C3×D411yescharacteristic
375C2×SD16C3×D411yescharacteristic
376C2×SD16C3×D411yescharacteristic
377C2×D8—21no—
378C2×D8—21no—
379C2×D8C3×D411yescharacteristic
380C2×D8C3×D411yescharacteristic
381#131—41no—
382#131—41no—
383#131—41no—
384#131—41no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16C23×C311yescharacteristic
388C2×M16C23×C311yescharacteristic
389C2×M16C23×C311yescharacteristic
390C2×M16C23×C311yescharacteristic
391C22×C8—21no—
392C22×C8—21no—
393C22×C8C23×C311yescharacteristic
394C22×C8C23×C311yescharacteristic
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—41no—
408#121—41no—
409#121—41no—
410C2×C4⋊C4C23×C311yescharacteristic
411C2×C4⋊C4C23×C311yescharacteristic
412C2×C4⋊C4C23×C311yescharacteristic
413C2×C22⋊C4—41no—
414C2×C42C23×C311yescharacteristic
415#107—21no—
416#107—21no—
417#106—21no—
418#106—21no—
419#104—41no—
420#104—41no—
421#104—41no—
422#104—41no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#100—41no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#95—41no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—22no—
450C23×C3—44no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—81no—
454C23×C3—81no—
455C23×C3—161no—
456C23×C3—161no—
457C23×C3H(5,𝔽2)11yescharacteristic
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—44no—
477C3×D4—44no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—161no—
489C3×D4—161no—
490C3×D4—161no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—44no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—81no—
511C2×C3×C4—81no—
512C2×C3×C4—81no—
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C22×D411yescharacteristic
515C2×C3×C4C2×#4111yescharacteristic
516C2×C3×C4H(5,𝔽2)11yescharacteristic
517C2×C3×C4H(5,𝔽2)11yescharacteristic
518C2×C3×C4H(5,𝔽2)11yescharacteristic
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—41no—
525C3×C8—41no—
526C3×C8—41no—
527C24—21no—
528C24—41no—
529#41—21no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—21no—
541#41—21no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—42no—
546#41—42no—
547#41—42no—
548#41—42no—
549C2×Q8C2×C3×D411yescharacteristic
550C2×Q8C2×C3×D411yescharacteristic
551C2×Q8C2×C3×D411yescharacteristic
552C2×Q8C2×C3×D411yescharacteristic
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4C2×C3×D411yescharacteristic
574C2×D4C2×C3×D411yescharacteristic
575C2×D4C2×C3×D411yescharacteristic
576C2×D4C2×C3×D411yescharacteristic
577C2×D4C3×#4112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4C24×C311yescharacteristic
588Q16—41no—
589Q16—41no—
590SD16—41no—
591SD16—41no—
592SD16—41no—
593SD16—41no—
594SD16—42no—
595SD16—42no—
596D8—41no—
597D8—41no—
598D8—42no—
599D8—42no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—42no—
609M16—42no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C2×C8—42no—
620C2×C8C2×C3×D411yescharacteristic
621C2×C8C2×C3×D411yescharacteristic
622C2×C8C2×C3×D411yescharacteristic
623C2×C8C2×C3×D411yescharacteristic
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C22⋊C4—82no—
640C42—21no—
641C42—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—82no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—161no—
661C22×C3—164no—
662C22×C3#53811yescharacteristic
663C22×C3D4211yescharacteristic
664C22×C3#56011yescharacteristic
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—81no—
670C3×C4—81no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4#53411yescharacteristic
674C3×C4#53411yescharacteristic
675C3×C4#54611yescharacteristic
676C3×C4#54611yescharacteristic
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—44no—
683C23—41no—
684C23—41no—
685C23—81no—
686C23—81no—
687C23—161no—
688C23—161no—
689C23C3×H(5,𝔽2)11yescharacteristic
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—22no—
705D4—22no—
706D4—21no—
707D4—21no—
708D4—44no—
709D4—44no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—161no—
721D4—161no—
722D4—161no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4C22×C3×D411yescharacteristic
746C2×C4C22×C3×D411yescharacteristic
747C2×C4C2×C3×#4111yescharacteristic
748C2×C4C3×H(5,𝔽2)11yescharacteristic
749C2×C4C3×H(5,𝔽2)11yescharacteristic
750C2×C4C3×H(5,𝔽2)11yescharacteristic
751C8—21no—
752C8—21no—
753C8—21no—
754C8—21no—
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—81no—
762C2×C3—81no—
763C2×C3—81no—
764C2×C3—81no—
765C2×C3—82no—
766C2×C3#266811yescharacteristic
767C2×C3#328811yescharacteristic
768C2×C3#329011yescharacteristic
769C22—21no—
770C22—21no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—82no—
785C22—81no—
786C22—81no—
787C22—161no—
788C22—164no—
789C22C3×#53811yescharacteristic
790C22C3×D4211yescharacteristic
791C22C3×#56011yescharacteristic
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4C3×#53411yescharacteristic
801C4C3×#53411yescharacteristic
802C4C3×#54611yescharacteristic
803C4C3×#54611yescharacteristic
804C3#3043111yescharacteristic, direct product factor, Sylow
805C2—21no—
806C2—21no—
807C2—81no—
808C2—81no—
809C2—81no—
810C2—81no—
811C2—82no—
812C2C3×#266811yescharacteristic
813C2C3×#328811yescharacteristic
814C2C3×#329011yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#3061C2semidirect
2. C3×#3060C2semidirect
3. C3×#3012C2semidirect
4. C3×#3012C2semidirect
5. C3×#2092C2semidirect
6. C3×#2079C2semidirect
7. C3×#2078C2semidirect
8. C3×#2040C2semidirect
9. C3×#2040C2semidirect
10. C3×#2006C2semidirect
11. C3×#1907C2semidirect
12. C3×#1907C2semidirect
13. C3×#1876C2semidirect
14. C3×#1876C2semidirect
15. C3×#1792C2semidirect
16. #30431C3direct (N × H)
22. C2×C3×#131C22semidirect
23. C2×C3×#131C22semidirect
26. C3×#537C22semidirect
43. C2×C3×#107C22semidirect
44. C2×C3×#106C22semidirect
47. C2×C3×#104C22semidirect
48. C2×C3×#104C22semidirect
53. C3×#417C22semidirect
54. C3×#417C22semidirect
61. C3×#382C22semidirect
62. C3×#343C22semidirect
63. C3×#343C22semidirect
64. C3×#343C22semidirect
65. C3×#341C22semidirect
66. C3×#341C22semidirect
67. C3×#336C22semidirect
68. #3061C2×C3semidirect
69. #3060C2×C3semidirect
70. #3012C2×C3semidirect
71. #3012C2×C3semidirect
72. #2092C2×C3semidirect
73. #2079C2×C3semidirect
74. #2078C2×C3semidirect
75. #2040C2×C3semidirect
76. #2040C2×C3semidirect
77. #2006C2×C3semidirect
78. #1907C2×C3semidirect
79. #1907C2×C3semidirect
80. #1876C2×C3semidirect
81. #1876C2×C3semidirect
82. #1792C2×C3semidirect
186. C2×#131C22×C3semidirect
187. C2×#131C22×C3semidirect
190. #537C22×C3semidirect
207. C2×#107C22×C3semidirect
208. C2×#106C22×C3semidirect
211. C2×#104C22×C3semidirect
212. C2×#104C22×C3semidirect
217. #417C22×C3semidirect
218. #417C22×C3semidirect
225. #382C22×C3semidirect
226. #343C22×C3semidirect
227. #343C22×C3semidirect
228. #343C22×C3semidirect
229. #341C22×C3semidirect
230. #341C22×C3semidirect
231. #336C22×C3semidirect
804. C3#30431direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#30612
C3×#30602
C3×#30122
C3×#20922
C3×#20792
C3×#20782
C3×#20402
C3×#20062
C3×#19072
C3×#18762
C3×#17922
#304313